Core Concepts
The author proposes an efficient algorithm, Fast Iterative Region Inflation (FIRI), to compute large convex polytopes with high quality and efficiency. FIRI balances managibility, computational efficiency, and high-quality results in generating convex regions.
Abstract
The content introduces the Fast Iterative Region Inflation (FIRI) algorithm for computing large convex polytopes efficiently. FIRI ensures managibility, computational efficiency, and high-quality results by iteratively inflating ellipsoids and calculating Maximum Volume Inscribed Ellipsoid (MVIE). The proposed algorithm addresses challenges faced by existing methods in generating convex free regions.
Key points include:
- Importance of compact representation and convexity in characterizing passable regions.
- Challenges in balancing quality and efficiency in generating large convex polytopes.
- Introduction of the concept of managibility in generating convex regions.
- Proposal of the FIRI algorithm that iteratively inflates ellipsoids to generate obstacle-free convex polytopes.
- Detailed explanation of Restrictive Inflation and MVIE calculation steps within FIRI.
- Comparison with existing algorithms like IRIS, RILS, and Parallel Convex Cluster Inflation.
- Contributions of FIRI including managibility assurance, efficient solver design, and comprehensive performance evaluation.
Stats
High-quality convex free polytope refers to be as large as possible in this paper.
Achieving a speedup of orders of magnitude compared to IRIS.
Quotes
"An ideal algorithm for computing free convex polytope should possess both managibility and computational efficiency."
"FIRI ensures managibility by restricting the halfspaces that compose the polytope."